What does this equation mean?

The scale of that abstract argument, made concrete decades later, is stark. Gholami and colleagues, surveying twenty years of server hardware, report that peak hardware FLOPS scaled at roughly 3.0 times every two years while DRAM bandwidth scaled at only 1.6 times and interconnect bandwidth at 1.4 times over the same interval [ 13 ] . Those are compounding rates, and compounding rates diverge violently over long periods. If the two multipliers applied uniformly across a full twenty years — an extrapolation the source itself does not perform, offered here only to size the shape of the problem, not as a number the cited paper states — the ratio between available arithmetic and available bandwidth grows as $\frac{\text{compute}(t)}{\text{bandwidth}(t)} \;=\; \frac{\text{compute}(0)}{\text{bandwidth}(0)} \cdot \left(\frac{3.0}{1.6}\right)^{t/2}$. with t measured in years. At t = 20 that factor works out to (3.0/1.6)^{10} $\approx$ 540 : a roughly five-hundredfold widening of the gap in raw compounding terms, and that is before accounting for the interconnect term separately. No single memory technology closes a gap shaped like that on its own. Every technology discussed below narrows it at one particular tier, for one particular class of workload, for a while — which is exactly why the industry kept needing a new one.